We present a unified lattice theory for a binary solution where endgro
ups are treated differently from middle groups. This is a simple examp
le of a triblock and the present study provides a starting point for s
tudying a general triblock system. We replace the original homogeneous
lattice by a Bethe lattice of the same coordination number as the ori
ginal lattice. The model is solved exactly on the Bethe lattice. The r
esulting solution goes beyond the random mixing approximation and prov
ides us with an approximate theory of the model on the regular lattice
. The contributions of endgroups on various thermodynamic properties o
f a binary solution are investigated in a quantitative way using the t
heory. In particular, our theory predicts that contributions to the en
ergy are more important than to the entropy. (C) 1997 American Institu
te of Physics.